Precalculus Examples

$y = - \frac{1}{2} x + 18$ , $y = - x + 20$

Step 1

Eliminate the equal sides of each equation and combine.

$- \frac{1}{2} x + 18 = - x + 20$

Step 2

Solve $- \frac{1}{2} x + 18 = - x + 20$ for $x$ .

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Step 2.1

Combine $x$ and $\frac{1}{2}$ .

$- \frac{x}{2} + 18 = - x + 20$

Step 2.2

Move all terms containing $x$ to the left side of the equation.

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Step 2.2.1

Add $x$ to both sides of the equation.

$- \frac{x}{2} + 18 + x = 20$

Step 2.2.2

To write $x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{x}{2} + x \cdot \frac{2}{2} + 18 = 20$

Step 2.2.3

Combine $x$ and $\frac{2}{2}$ .

$- \frac{x}{2} + \frac{x \cdot 2}{2} + 18 = 20$

Step 2.2.4

Combine the numerators over the common denominator.

$\frac{- x + x \cdot 2}{2} + 18 = 20$

Step 2.2.5

Add $- x$ and $x \cdot 2$ .

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Step 2.2.5.1

Reorder $x$ and $2$ .

$\frac{- x + 2 \cdot x}{2} + 18 = 20$

Step 2.2.5.2

Add $- x$ and $2 \cdot x$ .

$\frac{x}{2} + 18 = 20$

Step 2.3

Move all terms not containing $x$ to the right side of the equation.

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Step 2.3.1

Subtract $18$ from both sides of the equation.

$\frac{x}{2} = 20 - 18$

Step 2.3.2

Subtract $18$ from $20$ .

$\frac{x}{2} = 2$

Step 2.4

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 \cdot 2$

Step 2.5

Simplify both sides of the equation.

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Step 2.5.1

Simplify the left side.

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Step 2.5.1.1

Cancel the common factor of $2$ .

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Step 2.5.1.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 \cdot 2$

Step 2.5.1.1.2

Rewrite the expression.

$x = 2 \cdot 2$

Step 2.5.2

Simplify the right side.

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Step 2.5.2.1

Multiply $2$ by $2$ .

$x = 4$

Step 3

Evaluate $y$ when $x = 4$ .

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Step 3.1

Substitute $4$ for $x$ .

$y = - (4) + 20$

Step 3.2

Simplify $- (4) + 20$ .

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Step 3.2.1

Multiply $- 1$ by $4$ .

$y = - 4 + 20$

Step 3.2.2

Add $- 4$ and $20$ .

$y = 16$

Step 4

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(4, 16)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(4, 16)$

Equation Form:

$x = 4, y = 16$

Step 6